Year: 2024
Type: article
Abstract: We present the spin-wave theory of the excitation spectrum and quench dynamics of the non-Hermitian transverse-field Ising model. The complex excitation spectrum is obtained for a generic hypercubic lattice using the linear approximation of the Holstein-Primakoff transformation together with the complex bosonic Bogolyubov transformation. In the one-dimensional case, our result compares very well with the exact quasiparticle dispersion relation obtained via a fermionic representation of the problem, at least in the regime of large dissipation and transverse field. When applied to the quench dynamics, however, we show that the linear spin-wave approximation breaks down and the bosonic theory is plagued by a divergence at finite times. We understand the origin of this instability using a single-mode approximation. While limited to short times, we show that this approach allows us to characterize the dynamics arising from the quench of the dissipative term and the light-cone structure of the propagation quantum correlations. Furthermore, for the one-dimensional case, the linear spin-wave dynamics shows good agreement with the exact fermionic solution, both for the local magnetization and the spin-spin correlations.
Authors: Julien Despres, Leonardo Mazza, Marco Schirò
Institutions: Collège de France, Université Paris-Saclay
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402168206